随机派系网络模型统计性质研究

Statistics and analysis of the random cliques networks

提出派系作为构建复杂网络的基本模体,在随机选择规则下,采用自然增长方式构建随机派系网络的方法,并比较分析在此方式下网络的度分布、平均路径长度和聚类系数.研究发现随机派系网络的度分布服从多重泊松分布,且派系大小n越大,分层越多;随机派系网络相比于ER随机网络具有更高的聚类系数,且派系大小n越大,聚类系数越大;随机派系网络相比于ER随机网络具有更短的平均路径长度,且派系大小n越大,平均路径长度越短.随机派系网络模型是一个具有高的聚类系数和短的平均路径长度的网络模型,可以较好地描述现实中的复杂网络的高聚类小世界的性质,它为小世界网络模型的构建提供一种新的思路.

We proposed cliques as the basic motif for constructing complex networks.Under the random selection rules,natural growth was used to construct random clique networks,and the degree distribution,average path length and clustering coefficient of the network under this method were compared and analyzed.The study found that the degree distribution of the random clique network obeyed the multiple Poisson distribution,and the larger the clique size n,the more stratification;the random clique network had a higher clustering coefficient than the ER random network,and the larger the clique size n,the larger the clustering coefficient was;the random clique network had a shorter average path length than the ER random network,and the larger the clique size n,the shorter the average path length.The random clique network model was a network model with high clustering coefficient and short average path length.It can better describe the nature of the high-clustering small world of complex networks in reality.It provides a new way of thinking for the construction of small world network models.